I found this question in HRW (sixth edition), one of the 'checkpoints' (checkpoint 2, to be precise) in chapter 12 on 'rolling, torque, and angular momentum':(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Disks A and Bare identical and roll across a floor with equal speeds. The disk A roll up an incline, reaching a maximum height h, and the disk B moves up an incline that is identical except that it is frictionless. Is the maximum height reached by disk B greater than, less than, or equal to h?

2. Relevant equations

Work - Kinetic Energy Theorem

Concept of External Forces and Energy Changes (Potential and Kinetic) in a System

Newton's Second Law for Rotation

3. The attempt at a solution

I assumed the disks to lose all their kinetic energy at the maximum height (no more rotation, and no more translation).

So, for disk A, the (negative) work done by gravity (which comes out to be equal to mgh), and the (positive) work done by friction will equal the change in kinetic energy (which should be equal to 0.5{I[w]^2 + m[v]^2}, the rotational and translational kinetic energy.

For disk B, the equation will be [mgh = rotational + translational kinetic energy].

Because of the term pertaining to friction in A's equation, A's height comes out to be greater.

But, in the sample problem immediately after that, it explains that frictional force cannot do any work on a body rolling smoothly down an incline (what?!). But if this is true, friction would never make any difference to a body's rolling motion, so both should reach the same height...yet, the correct answer is that A will reach a greater height.

How?

Please help.

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# Homework Help: Friction and Rolling Analytical Question

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